
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
The graphs of \( y = |x| \) and \( y = -x^2 - 5x - 4 \) are drawn. For every \( x \), a vertical segment connecting these two graphs can be drawn as well. Find the smallest possible length of one of these vertical segments.

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