
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 $a_{1}=3$, $a_{2}=46$, and ${a_{n+2}}=\sqrt{{a_{n+1}}{a_n}-\frac{π}{{{a_{n+1}}}}}$, $\left(\pi \approx 3.14\right)$, find the maximum number of terms in this sequence.

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