
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 $\left\{a_{n}\right\}$ be a geometric sequence with all positive terms, and
$$
S=a_{1}+a_{2}+\cdots+a_{n}, \quad T=\frac{1}{a_{1}}+\frac{1}{a_{2}}+\cdots+\frac{1}{a_{n}}.
$$
Find the product of the first $n$ terms of $\left\{a_{n}\right\}$.

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