
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 $\{a_n\}$ where $a_1 = \frac{5}{6}, a_2 = \frac{19}{36}$, and a sequence $\{b_n\}$ which is an arithmetic sequence with a common difference of -1, where $b_n = \log_2(a_{n+1} - \frac{a_n}{3})$. 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 of the sequence $\{a_n\}$.

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