
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 $\{a\_n\}$ where all terms are positive numbers, and it satisfies $a\_2=5$, $a\_{n+1}=a\_n^2-2na\_n+2,(n∈N*)$.
(1) Deduce the general term formula of the sequence;
(2) If $b\_n=2^{n-1}$, let $c\_n=a\_n+b\_n$, find the sum of the first $n$ terms of the sequence $T\_n$.

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