
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 $\triangle ABC$, $P$ is the midpoint of the line $AD$ in $\triangle ABC$. The line $MN$ passing through point $P$ intersects side $AB$ at point $M$ and side $AC$ at point $N$. It is given that $\overrightarrow{AB}=m\overrightarrow{AM}$ and $\overrightarrow{AC}=n\overrightarrow{AN}$. Find the value of $m+n$.

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