
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
Find the number of the subsets  $B$  of the set  $\{1,2,\cdots, 2005 \}$  such that the sum of the elements of  $B$  is congruent to  $2006$  modulo  $2048$ 

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