
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
The sequence $\{a_n\}$ is an arithmetic sequence, with $a_1=f(x+1)$, $a_2=0$, $a_3=f(x-1)$, where $f(x)=x^2-4x+2$,

(1) Find the general formula for $a_n$;

(2) If $\{a_n\}$ is an increasing sequence, and $b_n= \frac{a_n+4}{4\times3^n}$, the sum of the first $n$ terms of the sequence $\{b_n\}$ is $T_n$, and for any $n\in\mathbb{N}^*$, it holds that $T_n > \log_m 2$, find the range of the real number $m$.

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