
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 parallelogram $ABCD$, point $M$ is on $\overline{AB}$, such that $\frac{AM}{MB} = \frac{2}{5}$, and point $N$ is on $\overline{AD}$, such that $\frac{AN}{ND} = \frac{2}{5}$. Let $P$ be the point of intersection between $\overline{AC}$ and $\overline{MN}$. Calculate $\frac{AP}{PC}$.

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