
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
The natural numbers  $m$  and  $k$   satisfy the equality   $$ 1001 \cdot 1002 \cdot  ... \cdot 2010 \cdot 2011 = 2^m (2k + 1) $$  . Find the number  $m$ .

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