
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 system of equations \(\left\{
\begin{array}{l}
x^{2} + y^{2} = 1 \\
\frac{|x-0.5| + |y| - a}{\sqrt{3} y - x} = 0
\end{array}
\right.\) has at least one solution. Indicate the number of distinct solutions of this system for each found value of the parameter \( a \).

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