
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 triangle $\triangle ABC$ with angles $A$, $B$, $C$ and the opposite sides $a$, $b$, $c$ respectively, it is known that $a\sin A\sin B + b\cos^2 A = \frac {4}{3}a$.
(1) Find the value of $\frac{b}{a}$.
(2) If $c^2 = a^2 + \frac{1}{4}b^2$, find the measure of angle $C$.

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