
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
A point has rectangular coordinates \((x,y,z)\) and spherical coordinates \(\left(3, \frac{6 \pi}{5}, \frac{\pi}{4}\right)\). Find the spherical coordinates of the point with rectangular coordinates \((-y,x,-z)\). Enter your answer in the form \((\rho, \theta, \phi)\), where \(\rho > 0\), \(0 \le \theta < 2\pi\), and \(0 \le \phi \le \pi\).

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