
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 in $\triangle ABC$, the sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively, and $a\cos B + \sqrt{3}b\sin A = c$.
(I) Find the measure of angle $A$;
(II) If $a=1$ and $\overrightarrow{AB} \cdot \overrightarrow{AC} = 3$, find the value of $b + c$.

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