
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
In the Cartesian coordinate system, the region composed of points located between the lines $y=k$ and $y=l$ (where $k$ and $l$ are constants, and $k<l$), including the lines $y=k$ and $y=l$, is called a "k⊕l type band region". Suppose $f(x)$ is a quadratic function, and three points $(-2, f(-2)+2)$, $(0, f(0)+2)$, $(2, f(2)+2)$ all lie within the "0⊕4 type band region". If the point $(t, t+1)$ lies within the "-1⊕3 type band region", then the maximum value of the function $y=|f(t)|$ is

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