
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
A robot on a plane always maintains a shorter distance to the point F(1, 0) than to the line x = -2 by 1 unit as it moves. If the robot cannot touch the line passing through point P(-1, 0) with a slope of k, determine the range of values for k.

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