
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 the arithmetic sequence $\left\{ a_n \right\}$, it is known that the common difference $d=2$, and $a_2$ is the geometric mean of $a_1$ and $a_4$.

(1) Find the general formula for the sequence $\left\{ a_n \right\}$.

(2) Let $b_n = a_{\frac{n(n+1)}{2}}$, and denote $T_n = -b_1 + b_2 - b_3 + b_4 - \cdots + (-1)^n b_n$, find $T_n$.

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