
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 uniformly made cube has its six faces numbered with \\(0\\), \\(1\\), \\(2\\), \\(3\\), \\(4\\), \\(5\\), and a uniformly made tetrahedron has its four vertices numbered with \\(1\\), \\(2\\), \\(3\\), \\(4\\). When this cube and tetrahedron are thrown at the same time, the number on the top face of the cube is \\(a\\), and the sum of the numbers on the three side faces of the tetrahedron is \\(b\\).
\\((1)\\) Find the probability of the event \\(b=3a\\);
\\((2)\\) Find the probability of the event "The point \\((a,b)\\) satisfies \\(a^2+(b-5)^2 \leqslant 9\\)".

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