
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 sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively. Given that $(2b - \sqrt{3}c)\cos A = \sqrt{3}a\cos C$.

1. Find the measure of angle $A$.
2. If angle $B = \frac{\pi}{6}$ and the length of the median $AM$ on side $BC$ is $\sqrt{7}$, find the area of triangle $ABC$.

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