
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
Given that point P is the center of the regular hexagon ABCDEF, and Z is the midpoint of the side AB, determine the fraction of the area of the hexagon that is in the smaller region created by segment ZP.

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