
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
Why are the equations $\boldsymbol{A}^{2}=\boldsymbol{B}^{2}$ (1) and $\boldsymbol{A}=\boldsymbol{B}$ (2), where $\boldsymbol{A}$ and $\boldsymbol{B}$ are known functions of $x$, generally not equivalent?

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