
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
 $\boxed{\text{A5}}$  Determine all positive integers  $a,b$  such that  $a^{2}b^{2}+208=4([a,b]+(a,b))^2$        where  $[a,b]$ -lcm of  $a,b$  and  $(a,b)$ -gcd of  $a,b$ .

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