
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 that $\cos\left(\alpha + \frac{2}{3}\pi\right) = \frac{4}{5}$ with $-\frac{\pi}{2} < \alpha < 0$, find the value of $\sin\left(\alpha + \frac{\pi}{3}\right) + \sin\alpha$.

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