
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 $\sin x + \cos x = \frac{1}{3}$, and $x$ is an angle in the second quadrant.  
Find (1) $\sin x - \cos x$  
(2) $\sin^3 x - \cos^3 x$.

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