
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
Through a fixed point in space, planes are drawn to divide the space into the maximum possible number of regions. One plane divides space into two parts, two intersecting planes divide it into four parts, and three planes that all intersect at one point and do not have any other common point divide the space into eight parts. What is the maximum number of regions that can be obtained with four planes? And with \( n \) planes?

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