
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
Given that a fair dice is rolled twice and the outcomes are denoted as $m$ and $n$ respectively. Let $a=(m,n)$ and $b=(1,-3)$ be two vectors in the plane.

(1) Find the probability that event "$a \perp b$" occurs.
(2) Find the probability that event "$|a| \leq |b|$" occurs.

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