
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 $a, b, c$ are real numbers, and the set $A=\left\{\sin a, \cos b, 0, 1, -2, \frac{\sqrt{2}}{2}, \ln c\right\}$, and the set $B=\left\{x \mid x=a^{2022} + a^2, a \in A\right\}$, if $|B|=4$, find the value of $\cos (2a) - \cos (2b) + c$.

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