
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, excluding row 0 and row 1, consist only of even numbers (with the exception of the 1's at either end). Recall that each number in Pascal's triangle is the sum of the two numbers above it.

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