
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

\[
\begin{cases}
5|x| + 12|y| = 60 \\
x^2 + y^2 - 2y + 1 - a^2 = 0
\end{cases}
\]

a) has exactly 3 solutions;

b) has exactly 2 solutions.

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