
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
Among all ordered pairs of real numbers  $(a, b)$  satisfying  $a^4 + 2a^2b + 2ab + b^2 = 960$ , find the smallest possible value for  $a$ .

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