<｜begin▁of▁sentence｜>### Instruction:
Imagine we're organizing a community leisure activity, much like crafting a vibrant mosaic with a variety of colored pieces. Each individual piece represents a participant in our program coming from different walks of life, symbolizing our data points scattered across a two-dimensional space. Now, our goal is to bring harmony to this mosaic, grouping these pieces into clusters that epitomize the diverse backgrounds and interests of our participants, akin to how multiple Gaussian distributions create our blobs.

Just as we adapt and tailor our programs to meet the individuals' unique preferences and requirements in recreational therapy, we seek to employ the 'KMeansCluster' method from the 'graspologic.cluster' API to discern these natural groupings, akin to identifying distinct interest groups within our participants. Can we determine the optimal arrangement of our mosaic—that is, the optimal number of clusters—to ensure each piece falls into a place where it resonates best with others, much like ensuring each participant is engaged in an activity that aligns with their interests and contributes to their well-being?

Our endeavor is to thoughtfully assign each participant, or data point, to its rightful cluster, enhancing the cohesion of our community activity and ensuring each individual is part of a group where they feel most connected and full of life. How might we best go about this intricate task, using the tools of 'KMeansCluster' to create an inclusive, supportive environment within our program?
### Response:
```python
from graspologic.cluster import KMeansCluster
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt

# Generate synthetic 2-dimensional data with 3 blobs
n_samples = 150
centers = [[1, 1], [-1, -1], [1, -1]]
cluster_std = [0.5, 0.5, 0.5]
X, y_true = make_blobs(n_samples=n_samples, centers=centers, cluster_std=cluster_std, random_state=42)

# Instantiate and fit the KMeans clusterer
c = KMeansCluster(max_clusters=5, random_state=42)
c.fit(X)

# Predict cluster labels based on the best model determined by KMeansCluster
labels = c.fit_predict(X)

# Plot the data points with cluster labels
plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='viridis')
plt.title('KMeans Clustered Data')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.show()
```
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