
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
Determine the set of values of \( m \) for which \( x^2 + 5xy + 2x + my - 2m \) has two factors, with integer coefficients, which are linear in \( x \) and \( y \).
**A)** \( 0, 10 \)  
**B)** \( 0, 5 \)  
**C)** \( 0, 1 \)  
**D)** \( 0, 20 \)  
**E)** \( 10, -10 \)

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