
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
Replace the odd numbers in Pascal's triangle with \\(1\\) and the even numbers with \\(0\\) to get the \\(0-1\\) triangle number table shown below. Counting from the top, the first time the entire row consists of \\(1\\)s is the first row, the second time the entire row consists of \\(1\\)s is the third row, \\(\ldots\\), the \\(n\\)th time the entire row consists of \\(1\\)s is the \\(\boxed{2^{n}-1}\\)th row.

First row:          \\(1\\)

Second row:        \\(1\\)  \\(0\\)  \\(1\\)

Third row:      \\(1\\)  \\(1\\)  \\(1\\)  \\(1\\)

Fourth row:    \\(1\\)  \\(0\\)  \\(0\\)  \\(0\\)  \\(1\\)

Fifth row:  \\(1\\)  \\(1\\)  \\(0\\)  \\(0\\)  \\(1\\)  \\(1\\)

\\(\ldots\\)  \\(\ldots\\)  \\(\ldots\\) \\(\ldots\\)

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