
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 real numbers $a$, $b$, $c$, $d$, $e$ satisfy $(a+c)(a+d)=(b+c)(b+d)=e \neq 0$, and $a \neq b$. Find the value of $(a+c)(b+c)-(a+d)(b+d)$.

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