
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
A sequence of real numbers \(u_{1}, u_{2}, u_{3}, \ldots\) is determined by \(u_{1}\) and the following recurrence relation for \(n \geq 1\):
\[ 4 u_{n+1} = \sqrt[3]{64 u_{n} + 15}. \]

Describe, with proof, the behavior of \(u_{n}\) as \(n \rightarrow \infty\).

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