
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 a polynomial $A$ in terms of $x$, when $A-(x-2)^{2}=x(x+7)$, complete the following questions:<br/>$(1)$ Find the polynomial $A$;<br/>$(2)$ If $3^{x+1}=1$, find the value of the polynomial $A$.

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