
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
When \( m = -5, -4, -3, -1, 0, 1, 3, 23, 124, 1000 \), the equation \((2m + 1)x + (2 - 3m)y + 1 - 5m = 0\) yields 10 linear equations in \( x \) and \( y \). The common solution for these 10 equations is \( x = \quad \) \( y = \quad \).

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