
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
Determine how many of the first 30 rows of Pascal's triangle, starting from row 0, have the property that they consist of only even numbers except for the 1's at each end. Use knowledge of binary representation and parity rules.

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