
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
Three students propose their respective approaches to solve the problem: "For the inequality $x^{2} + 25 + \left|x^{3} - 5 x^{2}\right| \geq a x$ to hold for all $x \in [1,12]$, find the range of the real number $a$."

Student A says: "We just need the smallest value on the left side of the inequality to be no less than the largest value on the right side."

Student B says: "Transform the inequality into a function of $x$ on the left side, with only a constant on the right side, and find the extremum of the function."

Student C says: "Consider both sides of the inequality as functions of $x$ and plot their graphs."

Referring to the above approaches, what is the correct range of values for $a$?

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