
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 horizontal sections of a right octagonal pyramid are obtained by slicing the pyramid with planes parallel to the octagonal base. The areas of these sections are $360$ square units and $810$ square units respectively. The two planes are $10$ units apart. Determine the distance from the apex to the larger section.

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