
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
The square \(ABCD\) has sides of length 105. The point \(M\) is the midpoint of side \(BC\). The point \(N\) is the midpoint of \(BM\). The lines \(BD\) and \(AM\) meet at the point \(P\). The lines \(BD\) and \(AN\) meet at the point \(Q\). What is the area of triangle \(APQ\)?

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