
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 $\frac{45x - 82}{x^2 - 5x + 6} = \frac{M_1}{x-2} + \frac{M_2}{x-3}$ be an identity in $x$. Find the numerical value of $M_1M_2$.
A) -264  
B) -424   
C) -342  
D) -365

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