
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 real number $a$ is chosen randomly and uniformly from the interval $[-15, 20]$. Find the probability that the roots of the polynomial
\[x^4 + 2ax^3 + (2a - 3)x^2 + (-4a + 5)x - 3\]
are all real.

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