
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 sides opposite angles $A$, $B$, $C$ are denoted as $a$, $b$, $c$, respectively, and it is given that $\cos(A- \frac {π}{3})=2\cos A$.
(1) If $b=2$ and the area of the triangle $ABC$ is $3 \sqrt {3}$, find the value of $a$;
(2) If $\cos 2C = 1 - \frac {a^{2}}{6b^{2}}$, determine the measure of angle $B$.

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