
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 $f$ and $g$ be quadratic functions for which $g(x) = -f(90 - x)$, and the graph of $g$ passes through the vertex of the graph of $f$. If the x-coordinates of the four intercepts of these two graphs are $x_1$, $x_2$, $x_3$, and $x_4$, in increasing order, and it is known that $x_4 - x_3 = 110$, find $x_2 - x_1$.

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