
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 vectors $a=(2\lambda\sin x,\sin x+\cos x)$ and $b=(\sqrt{3}\cos x,\lambda(\sin x-\cos x))$ ($\lambda > 0$), the maximum value of the function $f(x)=a\cdot b$ is $2$.

    (1) Find the interval of monotonic decrease for the function $f(x)$;

    (2) In $\triangle ABC$, with the opposite sides of angles $A$, $B$, $C$ being $a$, $b$, $c$ respectively, and $\cos A=\frac{2b-a}{2c}$, if $f(A)-m > 0$ always holds, find the range of the real number $m$.

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