
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 sequence $\{a\_n\}$, where $a\_1= \frac {5}{6},a\_2= \frac {19}{36}$, and the sequence $\{b\_n\}$ is an arithmetic sequence with a common difference of $(-1)$, where $b\_n=\\log \_{2}(a\_{n+1}- \frac {a\_n}{3})$. The sequence $\{c\_n\}$ is a geometric sequence with a common ratio of $( \frac {1}{3})$, where $c\_n=a\_{n+1}- \frac {a\_n}{2}$. Find the general term formula for the sequence $\{a\_n\}$, i.e., $a\_n=$ _____ .

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