
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 the equation with respect to $x$, $\cos^2(x+\pi) - \sin x + a = 0$,
(1) If $x = \frac{5\pi}{6}$ is a solution of this equation, find the value of $a$;
(2) If this equation has a solution, determine the range of values for $a$.

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