
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 to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $(c-2a) \overrightarrow{AB}\cdot \overrightarrow{BC}=c \overrightarrow{BC}\cdot \overrightarrow{AC}$.
1. Find the measure of angle $B$.
2. Given $f(x)=\cos x(a\sin x-2\cos x)+1$, if $f(x)\leqslant f(B)$ for any $x\in R$, find the monotonically decreasing interval of the function $f(x)$.

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