
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 geometric sequence with positive terms $\{a_n\}$, the product of its first $n$ terms is denoted as $\pi_n$. It is known that $a_{m-1} \cdot a_{m+1} = 2a_m$ and $\pi_{2m-1} = 2048$. Find the value of $m$.

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