
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 $\sin\theta - \cos\theta = \frac{1}{2}$, find the values of the following expressions:
(1) $\sin\theta\cos\theta$;
(2) $\sin^3\theta - \cos^3\theta$;
(3) $\sin^4\theta + \cos^4\theta$.

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