
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
The line $\rho\cos\theta - \rho\sin\theta + a = 0$ shares a common point with the circle defined by the parametric equations $\begin{cases} x = -1 + 3\cos\theta \\ y = 2 + 3\sin\theta \end{cases}$ (where $\theta$ is the parameter). Determine the range of values that the real number $a$ could take.

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