
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
Consider an arithmetic sequence $\{a\_n\}$. Let $S\_n$ denote the sum of its first $n$ terms. If $a\_{m-1}+a\_{m+1}-a\_m^2=0 (m\geqslant 2, m\in\mathbb{N}^*)$, and $S\_{2m-1}=58$, solve for $m$.

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