
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 $y=x+\frac{t}{x}$, it is known that if the constant $t>0$, then the function is decreasing on the interval $(0,\sqrt{t}]$ and increasing on the interval $[\sqrt{t},+\infty)$.

(1) Given $f(x)=\frac{x^2-2x-4}{x+2}$, where $x\in[-1,1]$, use the above property to find the monotonic intervals and the range of the function $f(x)$.

(2) For the function $f(x)$ in (1) and the function $g(x)=-x-2a$, if for any $x\_1\in[-1,1]$, there always exists $x\_2\in[0,1]$ such that $g(x\_2)=f(x\_1)$ holds, find the value of the real number $a$.

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