
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 $\{a\_n\}$, it is known that $a\_3=5$, $a\_2+a\_6=14$, and $2^{a\_n}$, $2^{a_{n+1}}$, $2^{a_{n+2}}$ form a geometric sequence.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) If the sequence $\{b\_n\}$ satisfies $b\_n=a\_n-(-1)^{n}n$, and the sum of the first $n$ terms of the sequence $\{b\_n\}$ is $T\_n$, find $T\_21$.

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