
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
Find the sum of all angles \( x \) in \([0^\circ, 360^\circ]\) satisfying the equation:
\[ \sin^3 x + \cos^3 x = \frac{1}{\sin x} + \frac{1}{\cos x}. \]

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