
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 \(a\), \(b\), \(c\), and \(d\) be real numbers such that \(|a-b|=3\), \(|b-c|=4\), and \(|c-d|=5\). Additionally, \(a\) is fixed at 0. What is the sum of all possible values of \(|a-d|\)?

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