
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 $f(x)=2\cos x(\sin x-\cos x)+m(m\in R)$, the graph of $y=f(x)$ is translated to the left by $\frac{\pi }{4}$ units to obtain $y=g(x)$. The maximum value of $y=g(x)$ in the interval $[0,\frac{\pi }{4}]$ is $\sqrt{2}$.

(1) Find the value of the real number $m$;

(2) In $\Delta ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. If $g(\frac{3}{4}B)=1$ and $a+c=2$, find the range of the perimeter $l$ of $\Delta ABC$.

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