
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
(1) Simplify $\sin 119^\circ \sin 181^\circ - \sin 91^\circ \sin 29^\circ$.
(2) Given $\sin (\alpha - \beta) \cos \alpha - \cos (\alpha - \beta) \sin \alpha = \frac{3}{5}$, and $\beta$ is an angle in the third quadrant, find the value of $\sin (\beta + \frac{\pi}{4})$.

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