
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 $\left\{ a_n \right\}$ whose sum of the first $n$ terms $S_n$ satisfies $3S_n=1-a_n$, where $n \in N^*$.

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

(2) Let $b_n=\frac{1}{\log_{2}a_n \cdot \log_{2}a_{n+1}}$ $(n \in N^*)$, find the sum of the first $n$ terms $T_n$ of the sequence $\left\{ b_n \right\}$.

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