
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
Feeling excited over her successful explorations into Pascal's Triangle, Wendy formulates a second problem to use during a future Jupiter Falls High School Math Meet:

\[\text{How many of the first 2010 rows of Pascal's Triangle (Rows 0 through 2009)} \ \text{have exactly 256 odd entries?}\]
What is the solution to Wendy's second problem?

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