
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
Consider the polynomial $49x^3 - 105x^2 + 63x - 10 = 0$ whose roots are in arithmetic progression. Determine the difference between the largest and smallest roots.
A) $\frac{2}{7}$
B) $\frac{1}{7}$
C) $\frac{3\sqrt{11}}{7}$
D) $\frac{2\sqrt{11}}{7}$
E) $\frac{4\sqrt{11}}{7}$

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