
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
Margot writes the numbers \(1,2,3,4,5,6,7,\) and \(8\) in the top row of a table, as shown. In the second row she plans to write the same set of numbers, in any order. Each number in the third row is obtained by finding the sum of the two numbers above it. In how many different ways can Margot complete row 2 so that every entry in row 3 is even?

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