
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 \((x-a)^{2}-(y-b)^{2}=4(a^{2}+b^{2})\) and \((x+a)^{2}+(y+b)^{2}=4(a^{2}+b^{2})\) whose radii is \(\sqrt{a^{2}+b^{2}}\), determine the number of circles tangent to both.

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