
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 \( |a-b|=2 \), \( |b-c|=4 \), and \( |c-d|=5 \). Determine the sum of all possible values of \( |a-d| \).

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