
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 the diagram, $\triangle ABC$ has $\angle BAC = \angle BCA$. Given $BC=8$ and $AB=13$, what is the perimeter of $\triangle ABC$?
```plaintext
draw((0,0)--(6,10.39)--(12,0)--cycle);
label("8",(6,0),S);
label("$B$",(0,0),SW);
label("$C$",(12,0),SE);
label("$A$",(6,10.39),N);
label("13",(9,5.2));
```

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