
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 that $a > 0$, the maximum value of the function $f(x)=\cos x(2a\sin x-\cos x)+\sin ^{2}x$ is $2$.
(1) Find the monotonically decreasing interval of the function $f(x)$;
(2) In triangle $ABC$, the sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$ and $\frac {a^{2}+c^{2}-b^{2}}{a^{2}+b^{2}-c^{2}}= \frac {c}{2a-c}$, find the range of $f(x)$ on $\[B, \frac {π}{2}\]$.

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