
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
In the cube \( A B C D A' B' C' D' \) with an edge length of 1, the points \( T, P, \) and \( Q \) are the centers of the faces \( A A' B' B, A' B' C' D', \) and \( B B' C' C \) respectively. Find the distance from point \( P \) to the plane \( A T Q \).

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