
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 \( b \) for which there exists a number \( a \) such that the system

\[ 
\begin{cases} 
x^2 + y^2 + 2b(b - x + y) = 4 \\
y = 5 \cos(x - a) - 12 \sin(x - a)
\end{cases} 
\]

has at least one solution \((x, y)\).

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