
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
Given that $a$, $b$, and $c$ are the three side lengths of $\triangle ABC$, and $b$ and $c$ satisfy $\left(b-5\right)^{2}+\left(c-7\right)^{2}=0$, $a$ is a solution of the equation $|a-3|=2$. Find the perimeter of $\triangle ABC$ and determine the shape of $\triangle ABC$.

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