
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
Let the sequence \(a_1, a_2, a_3, \cdots\) be defined as follows: \(a_1 = 1\),
\[a_{n+1} = \frac{1}{16} \left(1 + 4a_n + \sqrt{1 + 24a_n}\right), \quad n = 1, 2, \cdots\]
Find its general term formula.

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