
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
Compute the determinant of the matrix:
\[
\begin{vmatrix} \sin (1+\frac{\pi}{4}) & \sin (2+\frac{\pi}{4}) & \sin (3+\frac{\pi}{4}) \\ \sin (4+\frac{\pi}{4}) & \sin (5+\frac{\pi}{4}) & \sin (6+\frac{\pi}{4}) \\ \sin (7+\frac{\pi}{4}) & \sin (8+\frac{\pi}{4}) & \sin (9+\frac{\pi}{4}) \end{vmatrix}
\]
where all angles are in radians.

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