
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 of equations \(\left\{\begin{array}{c}x \sin a - y \cos a = 2 \sin a - \cos a \\ x - 3y + 13 = 0\end{array}\right.\) have a solution \((x, y)\) within the square \(5 \leq x \leq 9,\: 3 \leq y \leq 7\)?

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