
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
A circle $C$ is defined by the equation $(x-1)^2 + (y+2)^2 = 25$. There are four distinct points on the circle that are each a distance of $2$ from the line $l: y = -\frac{4}{3}x - \frac{a}{3}$. Determine the range of possible values for $a$.

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