
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 \( h(0) = 2 \), for \( n \geq 1 \), \( h(n) > 0 \), and
\[ h^2(n) - 2 \cdot h^2(n-1) = 1, \]
find the general term formula for the sequence \( \{h(n)\}_{n \geq 0} \).

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