
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
When three standard dice are tossed, the numbers \(x, y, z\) appear sequentially. Find the probability that \(x, y, z\) are in an increasing arithmetic progression.

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