
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 two circles $C_{1}: x^{2}+y^{2}=4$ and $C_{2}: (x-4)^{2}+(y+a)^{2}=64$, where $a\in N^{*}$. If circles $C_{1}$ and $C_{2}$ have exactly $2$ common tangents, then the possible values of $a$ are ______ (provide one value that satisfies the condition).

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