
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
Let the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ be $S_n$. If there exist positive integers $m$, $n$ ($m < n$) such that $S_m = S_n$, then $S_{m+n} = 0$. By analogy with the above conclusion, let the product of the first $n$ terms of a positive geometric sequence $\{b_n\}$ be $T_n$. If there exist positive integers $m$, $n$ ($m < n$) such that $T_m = T_n$, then $T_{m+n} =$ ___.

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