
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 point is randomly thrown onto the segment [12, 17] and let \( k \) be the resulting value. Find the probability that the roots of the equation \((k^{2} + k - 90)x^{2} + (3k - 8)x + 2 = 0\) satisfy the condition \( x_{1} \leq 2x_{2} \).

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