
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 $\sin \alpha = \frac{3}{5}$ and $\alpha$ is an angle in the first quadrant, find the value of $\cos (\frac{\pi}{3} + \alpha)$. The options are:
A) $\frac{-4 - 3\sqrt{3}}{10}$
B) $\frac{4 - 3\sqrt{3}}{10}$
C) $\frac{3\sqrt{3} - 4}{10}$
D) $\frac{4 + 3\sqrt{3}}{10}$

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