
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
Player A and player B are playing a number-guessing game. First, player A thinks of a number, denoted as $a$, then player B guesses the number that player A was thinking of and denotes their guess as $b$. Both $a$ and $b$ are in the set $\{1, 2, 3, 4, 5, 6\}$. Let $x = |a - b|$.

(1) Calculate the probability that $x=1$.

(2) If $x \leq 1$, it is said that "player A and player B have a telepathic connection." Calculate the probability of "player A and player B having a telepathic connection."

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