
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
If  $f(x, y) = 3x^2 + 3xy + 1$  and  $f(a, b) + 1 = f(b, a) = 42$ , then determine  $|a + b|$ .

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