
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
In space, there are 3 planes and a sphere. In how many different ways can a second sphere be placed in space so that it touches the three given planes and the first sphere? (In this problem, spheres are considered to touch each other, not only externally.)

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