
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A piece of glass has a square shape with an area of 1. On both sides of this glass, maps are drawn, with five regions on each map. The regions on one side of the glass are colored using five different colors. It is required to color the regions on the opposite side of the glass with the same five colors such that: a) different regions are colored in different colors; and b) the total area of the sections of the glass colored in the same color on both sides is at least 1/5. Is this always possible to achieve?

Present the answer in LaTex format: \boxed{Your answer}
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