
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 $$\alpha, \beta \in \left( \frac{3\pi}{4}, \pi \right)$$, $$\sin(\alpha + \beta) = -\frac{7}{25}$$, and $$\sin\left(\beta - \frac{\pi}{4}\right) = \frac{4}{5}$$, find the value of $$\sin\left(\alpha + \frac{\pi}{4}\right)$$.

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