
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 \( a, b, c, d \) be real numbers such that
\[ \min (20 x+19, 19 x+20) = (a x + b) - |c x + d| \]
for all real numbers \( x \). Find \( ab + cd \).

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