
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
In the sequence of positive terms \(\{a_n\}\),
$$
a_1 = 10, \quad a_{k+1} = 10 \sqrt{a_k} \quad (k=1, 2, \ldots).
$$

Find the general formula for \(a_n\).

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