
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
Evaluate
\[
\begin{vmatrix} 
\cos (\alpha + \phi) \cos (\beta + \phi) & \cos (\alpha + \phi) \sin (\beta + \phi) & -\sin (\alpha + \phi) \\ 
-\sin (\beta + \phi) & \cos (\beta + \phi) & 0 \\ 
\sin (\alpha + \phi) \cos (\beta + \phi) & \sin (\alpha + \phi) \sin (\beta + \phi) & \cos (\alpha + \phi) 
\end{vmatrix}.
\]

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