
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 (starting from row 0) of Pascal's triangle contain only even numbers for entries other than the numbers at each end ('1'). Include an additional constraint: Do not count rows where any two consecutive internal entries are equal.

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