
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 the curve $C$: 
$$
\begin{cases} 
x=a+2\cos\theta \\
y=a+2\sin\theta 
\end{cases}
$$
(where $\theta$ is the parameter), determine the range of the real number $a$ for which the curve has exactly two points whose distance from the origin is $2$.

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