
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, $\triangle ABC$ is a right triangle with $\angle ABC = 90^\circ$ and $\angle BAC= \angle BCA$. If $AB = 9$ and $BC = 6$, determine the perimeter of $\triangle ABC$.
[asy]
draw((0,0)--(6,0)--(6,9)--cycle);
label("6",(3,0),S);
label("9",(6,4.5),E);
label("$A$",(6,9),N);
label("$B$",(6,0),SE);
label("$C$",(0,0),SW);
[/asy]

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