
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
Given that $a \in \mathbb{R}$, find the value of $a$ such that the line $ax - y + 2 = 0$ is tangent to the circle defined by the parametric equations $\begin{cases} x = 2 + 2\cos\theta, \\ y = 1 + 2\sin\theta \end{cases}$, where $\theta$ is a parameter.

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