
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 $\{a_n\}$ with $a_3 = -4$ and $a_1 + a_{10} = 2$,
(1) Find the general formula for the sequence $\{a_n\}$;
(2) If sequence $\{b_n\}$ satisfies $a_n = \log_{3} b_n$, and let $T_n = b_1 \cdot b_2 \cdot \ldots \cdot b_n$, for what value of $n$ is $T_n > 1$.

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