
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 system

$$
\left\{\begin{array}{c}
(x-8) \sin a-(y+2) \cos a=0 \\
\left((x-3)^{2}+(y-3)^{2}-1\right)\left((x-3)^{2}+(y-3)^{2}-9\right)=0
\end{array}\right.
$$

have four solutions?

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