
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
Through the center $O$ of the inscribed circle $\omega$ of triangle $A B C$, a line is drawn parallel to side $B C$, intersecting sides $A B$ and $A C$ at points $M$ and $N$ respectively. Given that $S_{ABC}=\sqrt{15}$, $BC=2$, and segment $AO$ is four times the radius of $\omega$. Find the perimeter of triangle $AMN$.

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