
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
In an arithmetic sequence $\\{a\_n\\}$, the common difference is $d=2$, and $a\_2$ is the geometric mean of $a\_1$ and $a\_4$.
(1) Find the general term formula of the sequence $\\{a\_n\\}$;
(2) Let $b\_n = a\_{\frac{n(n+1)}{2}}$, and define $T\_n = -b\_1 + b\_2 - b\_3 + b\_4 - \ldots + (-1)^n b\_n$, find $T\_n$.

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