
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 $f(x)=tx$, $(x∈R)$.
(1) If $t=ax+b$, $a$, $b∈R$, and $-1≤f(-1)≤2$, $2≤f(1)≤4$, find the area of the plane region represented by the set of points $(a,b)$;
(2) If $t=2+ \frac {1}{x^{2}-x}$, $(x < 1$ and $x≠ 0)$, find the maximum value of the function $f(x)$;
(3) If $t=x-a-3(a∈R)$, the solution set of the inequality $b^{2}+c^{2}-bc-3b-1≤f(x)≤a+4(b,c∈R)$ is $[-1,5]$, find the values of $b$, $c$.

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