
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 of positive terms \(\{a_n\}\) satisfying:
\[ 
a_1 = \frac{1}{2}, \quad a_{n+1}^2 = \frac{2a_n^2}{1 + 2a_n^2}.
\]

Find \(a_n =\).

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