
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 that the function $f(x)$ defined on $\mathbb{R}$ is an even function, when $x\geqslant 0$, $f(x)=x^{2}-4x$
(1) Find the value of $f(-2)$;
(2) Find the analytical expression of $f(x)$ when $x < 0$;
(3) Suppose the maximum value of the function $f(x)$ on $[t-1,t+1](t > 1)$ is $g(t)$, find the minimum value of $g(t)$.

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