
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
Define a new sequence $(a_n)$ with an initial condition $a_0 = 2$ and a recurrence relation given by $a_{n + 1} = \frac{2}{3}a_n + \frac{4}{3}\sqrt{9^n - a_n^2}$ for $n \geq 0$. Find $a_{10}$.

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