
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 triangle $ABC$, point $M$ is on $\overline{AB}$ so that $\frac{AM}{AB} = \frac{3}{25}$, and point $N$ is on $\overline{BC}$ such that $\frac{BN}{BC} = \frac{3}{14}$. Let $P$ be the point of intersection of $\overline{AC}$ and $\overline{MN}$. Find $\frac{AC}{AP}$.

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