
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 sequence ${a_n}$ with its first $n$ terms sum $S_n$, it is known that $a_1=2$, $a_2=8$, and $S_{n+1}+4S_{n-1}=5S_n (n\geqslant 2)$. $T_n$ is the first $n$ terms sum of the sequence ${\log_2 a_n}$.
(1) Find the general term formula of the sequence ${a_n}$;
(2) Find the maximum positive integer value of $n$ that satisfies $(1-\frac{1}{T_2})(1-\frac{1}{T_3})...(1-\frac{1}{T_n})>\frac{51}{101}$.

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