
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 the roots of the equation \((x-a)(x-b) = (x-c)(x-d)\) given that \(a + d = b + c = 2015\) and \(a \neq c\). The specific values of \(a, b, c,\) and \(d\) are not provided.

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