
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
Let $a$, $b$, $c$, $a+b-c$, $a+c-b$, $b+c-a$, $a+b+c$ be seven distinct prime numbers, and among $a$, $b$, $c$, the sum of two numbers is 800. Let $d$ be the difference between the largest and the smallest of these seven prime numbers. Find the maximum possible value of $d$.

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