
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 rows up to row 30 in Pascal's triangle have the property that all numbers, except for the ones on the ends, are odd. Include an analysis of rows that contain only even numbers for comparison.

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