
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
Let $\{a\_n\}$ be a geometric sequence, and $T\_n=na\_1+(n-1)a\_2…+2a\_{n-1}+a\_n$. Given $T\_1=1$ and $T\_2=4$,
(1) Find the first term and common ratio of the sequence $\{a\_n\}$;
(2) Find the general formula for the sequence $\{T\_n\}$.

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