
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 a triangle $\triangle ABC$ with interior angles $A$, $B$, and $C$, opposite sides are $a$, $b$, and $c$ respectively, and the following equation holds: $$ \frac {\cos A - 2\cos C}{\cos B} = \frac {2c-a}{b} $$.  
(1) If $C = A + \frac {\pi}{3}$, find the measure of angle $A$;  
(2) If $\cos B = \frac {1}{4}$ and the perimeter of $\triangle ABC$ is 5, find the value of $b$.

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