
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 spheres touch each other externally, and each of them touches a larger sphere internally. The radius of one sphere is half the radius of the largest sphere, and the radius of the other sphere is one-third the largest sphere's radius. At the point where the smaller spheres touch each other, a tangent plane to them is constructed. Find the distance from this plane to the center of the largest sphere, given that its radius is $R$.

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