
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
Let \( q(x) = x^2 + ax + b \), where \( a \) and \( b \) are integers. Determine \( q(2) \) if \( q(x) \) is a factor of both \( 2x^4 + 8x^2 + 50 \) and \( 6x^4 + 12x^2 + 56x + 20 \).

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