
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 a parallelogram $ABCD$, sides $AB = 15$, $BC = 20$, and diagonals $AC$ and $BD$ intersect at point $P$. It is known that the areas of triangles $\triangle APB$ and $\triangle CPD$ are equal, and $AC = 26$. Determine the length of $AP$.
A) 11
B) 12
C) 13
D) 14

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