
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 $a$ does the system 
\[
\left\{\begin{array}{l}
x \cos a + y \sin a = 5 \cos a + 2 \sin a \\
-3 \leq x + 2y \leq 7, \\
-9 \leq 3x - 4y \leq 1
\end{array}\right. 
\]
have a unique solution?

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