
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
Find all values of the parameter \( a \) for which the equation

\[ 
\frac{|\cos t - 0.5| + |\sin t| - a}{\sqrt{3} \sin t - \cos t} = 0 
\]

has at least one solution on the interval \([0, \pi / 2]\). Indicate the number of different solutions of this equation on the interval \([0, \pi / 2]\) for each found value of the parameter \( a \).

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