
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 straight line $y=x+m$ intersects the ellipse $({x}^{2}+4{y}^{2}=4)$ at points $A$ and $B$, find the maximum value of $|AB|$ (the distance between $A$ and $B$) as $m$ varies.

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