
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 the sequence \(c_{1}, c_{2}, \ldots, c_{n}, \ldots\) where \(c_{1}=1\) and

\[ c_{n+1} = \sqrt{2 \sqrt[3]{3 \sqrt[5]{5 c_{n}}}} \quad (n=1, 2, \ldots) \]

does this sequence converge?

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