
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 a geometric sequence $\{a_n\}$ with the product of its first $n$ terms denoted as $T_n$ ($n \in \mathbb{N}^*$). Given that $a_{m-1}a_{m+1} - 2a_m = 0$ and $T_{2m-1} = 128$, find the value of $m$.

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