
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
For which values of \(a\) does the equation \(\cos (x-a) - \sin (x+2 \alpha) = 0\) have two solutions \(x_{1}\) and \(x_{2}\) such that \(x_{1} - x_{2} \neq \pi k\), where \(k \in \mathbb{Z}\)?

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