
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
Given $b \neq c$ and $x \neq 0$, determine the arithmetic mean between $\frac{x + b}{x}$ and $\frac{x - c}{x}$.
A) $\frac{b - c}{2x}$
B) $1 + \frac{b - c}{2x}$
C) $1$
D) $\frac{x}{b - c}$
E) $2x$

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