
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 a regular triangular prism $ABC-A_{1}B_{1}C_{1}$ with a height of 2 and a base edge length of 1, the center of the top face regular triangle $A_{1}B_{1}C_{1}$ is $P$. A plane $BCD$ is perpendicular to $AP$ and intersects edge $AA_{1}$ at $D$. Find the area of the cross section $BCD$.

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