
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
Let the function $f(x) = (x^2 - 10x + c_1)(x^2 - 10x + c_2)(x^2 - 10x + c_3)(x^2 - 10x + c_4)(x^2 - 10x + c_5)$, and the set $M = \{x | f(x) = 0\} = \{x_1, x_2, \ldots, x_9\} \subseteq \mathbb{N}^*$. Given that $c_1 \geq c_2 \geq c_3 \geq c_4 \geq c_5$, calculate $c_1 - c_5$.

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