
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 with  $ |a\minus{}b|\equal{}2$ ,  $ |b\minus{}c|\equal{}3$ , and  $ |c\minus{}d|\equal{}4$ . Calculate the sum of all possible values of  $ |a\minus{}d|$ .

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