
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
A cube toy is labeled with numbers $1$, $2$, $3$, $4$, $5$, and $6$ on its six faces. Two students, A and B, play a game in which A first throws the cube and records the number $a$ on the top face, followed by B throwing the cube and recording the number $b$ on the top face. Given that $|a-b| \leqslant 1$, calculate the probability that the two players are "in sync".

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