
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
Two circles, \(\odot O_{1}\) and \(\odot O_{2}\), are externally tangent to each other with radii 7 and 14 respectively. A third circle \(\odot O_{3}\) that is tangent to both \(\odot O_{1}\) and \(\odot O_{2}\) has its center on the line connecting their centers. Find the radius of a fourth circle that is tangent to \(\odot O_{1}\), \(\odot O_{2}\), and \(\odot O_{3}\).

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