
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
Let  $k$  be a positive real number. Suppose that the set of real numbers  $x$  such that  $x^2+k|x| \leq 2019$  is an interval of length  $6$ . Compute  $k$ .

*Proposed by Luke Robitaille*

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