
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 that \( f(x) = p x^{6} + q x^{4} + 3x - \sqrt{2} \), and \( p, q \) are non-zero real numbers, if \( d = f(c) - f(-c) \), find the value of \( d \).

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