
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 the function $f(x)=2\sin ^{2}x+\cos ( \frac {π}{3}-2x)$.
(1) Find the interval where $f(x)$ is decreasing on $[0,π]$;
(2) In triangle $ABC$, let the sides opposite to angles $A$, $B$, $C$ be $a$, $b$, $c$ respectively. If $f(A)=2$, and vector $\overrightarrow{m}=(1,2)$ is collinear with vector $\overrightarrow{n}=(\sin B,\sin C)$, find the value of $\frac {a}{b}$.

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