
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
Given that
\[\frac{\cos^6 \theta}{\cos^2 \phi} + \frac{\sin^6 \theta}{\sin^2 \phi} = 1,\]
find the sum of all possible values of
\[\frac{\sin^6 \phi}{\sin^2 \theta} + \frac{\cos^6 \phi}{\cos^2 \theta}.\]

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