
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 positive term arithmetic sequence $\{a_n\}$ satisfying $a_{n+1} + a_{n-1} = a_n^2$ for $(n\geq2)$, and a geometric sequence $\{b_n\}$ satisfying $b_{n+1}b_{n-1} = 2b_n$ for $(n\geq2)$, calculate $\log_2(a_2 + b_2)$.

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