
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
The slant height of a cone is \( l \), and the angle between the slant height and the base is \( \theta \). Find the side length of the largest cube that can be inscribed in the cone where 4 vertices of the cube are on the base of the cone and the other 4 vertices are on the lateral surface of the cone.

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