
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
Consider a modified Pascal's triangle wherein each entry is not just the sum of two numbers directly above it, but the sum plus 2 (ignore the first row for this addition). Investigate if there are any rows among the first 30 rows, similar to the traditional Pascal's triangle, where all the numbers between the two 1s at the ends are even.

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