
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 an arithmetic sequence $\{a_n\}$, the sum of the first $n$ terms is $S_n$. If $m > 1$ and $a_{m-1} + a_{m+1} - a_m^2 - 1 = 0$, and $S_{2m-1} = 39$, find the value of $m$.

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