
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 \((a > -2)\), if circle \(O_{1}\): \(x^{2} + y^{2} + 2x - 2ay - 8a - 15 = 0\) and circle \(O_{2}\): \(x^{2} + y^{2} + 2ax - 2ay + a^{2} - 4a - 4 = 0\) always have a common point, determine the range of the real number \(a\).

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