
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
Non-negative integers  $a, b, c, d$  satisfy the equation  $a + b + c + d = 100$  and there
 exists a non-negative integer n such that  $$ a+ n =b- n= c \times n = \frac{d}{n}  $$  Find all 5-tuples  $(a, b, c, d, n)$  satisfying all the conditions above.

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