<｜begin▁of▁sentence｜>### Instruction:
As a Sleep Specialist, I often evaluate and treat various sleep disorders to improve the overall well-being of my patients. In a recent case, I worked with a patient who wanted to map their sleep patterns using a 2D Descartes coordinate system. To visualize the data points within the coordinate system, I need to draw a 400x400 pixel plot, setting the bounds to (0, 20, 0, 20). Additionally, the patient asked me to convert a local coordinate point (5, 5) to the plot context coordinate system and save the output to an image file. This will help them better understand their sleep patterns and make informed decisions about improving their sleep quality.
### Response:
import igraph
from igraph.drawing import Plot
from igraph.drawing.coord import DescartesCoordinateSystem

# Initialize the plot with a specific bounding box
plot = Plot(bbox=(400, 400), background='white')

# Create a Descartes coordinate system with specified bounds
coord_system = DescartesCoordinateSystem(plot.ctx, plot.bbox, (0, 10, 0, 10))

# Set new bounds
coord_system.bounds = (0, 20, 0, 20)

# Draw the coordinate system
coord_system.draw()

# Convert a point from the local coordinate system (Descartes) to the context
converted_point = coord_system.local_to_context((5, 5))

# Save the plot with the coordinate system
plot.save('coordinate_system.png')
<|EOT|>
