
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
On a cardboard, there are three natural numbers: 100, 200, and 400. If two additional natural numbers are written on the cardboard, and then from these five numbers, several (at least two) are selected to perform operations using only addition and subtraction, where each selected number can only appear once in the expression, what is the maximum number of distinct non-zero natural numbers \( k \) that can be obtained from all such operations?

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