
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
Find all values of the parameter \( a \) for which the set of solutions to the inequality \( x^{3} - (a^{2} + a + 1)x^{2} + (a^{3} + a^{2} + a)x - a^{3} \geqslant 0 \) is a ray.

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