
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
Find all quadruples  $(a, b, c, d)$  of non-negative integers such that  $ab =2(1 + cd)$  and there exists a non-degenerate triangle with sides of length  $a - c$ ,  $b - d$ , and  $c + d$ .

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