
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 1, and the angle that this slant height makes with the base is $\theta$. The edge length of the inscribed cube in this cone is ______. (The cube has 4 vertices on the base of the cone, and the other 4 vertices on the lateral surface of the cone).

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