
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
Determine the number of triples B needs to name to be sure of identifying the member (X,Y,Z) from the set of all triples (x,y,z) with non-negative integers \( x,y,z < 10 \):
B names a triple (a,b,c) in T. A replies with \( |X + Y - a - b| + |Y + Z - b - c| + |Z + X - c - a| \).

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