
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
For real numbers \( x \), \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \). Find the largest positive integer \( n \) such that the following equation holds:
\[
\lfloor \log_2 1 \rfloor + \lfloor \log_2 2 \rfloor + \lfloor \log_2 3 \rfloor + \cdots + \lfloor \log_2 n \rfloor = 1994
\]
(12th Annual American Invitational Mathematics Examination, 1994)

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