
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 $\cos(\theta + \frac{\pi}{6}) = \frac{5}{13}$ and $\theta \in (0, \frac{\pi}{2})$, find the value of $\cos(\theta)$.

A) $\frac{12 + 3\sqrt{3}}{26}$
B) $\frac{12 + 5\sqrt{3}}{26}$
C) $\frac{6 + 3\sqrt{3}}{13}$
D) $\frac{6 + 4\sqrt{3}}{13}$

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