
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
In $\triangle ABC$, the lengths of the sides opposite to angles $B$ and $C$ are $a$ and $b$ respectively, and it is given that $\sin(C + \frac{\pi}{6}) = \frac{b}{2a}$. Find the value of angle $A$.

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