
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 the function $f(x)= \sqrt {3}\cos{\pi x}-\sin{\pi x}$ on $x\in (0,1)$, its zero points form an arithmetic sequence $\{a\_n\}$ ($n\in\mathbb{N}^*$) with the first term $a\_1$, and the common difference $d=1$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) Let $b\_n=(\frac{1}{2})^{n}(a\_n+\frac{2}{3})$, find the sum of the first $n$ terms $T\_n$ of the sequence $\{b\_n\}$.

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