
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 \\(p\\): \\(4{x}^{2}+12x-7\leqslant 0 \\); \\(q\\): \\(a-3\leqslant x\leqslant a+3 \\).

\\((1)\\) When \\(a=0\\), if \\(p\\) is true and \\(q\\) is false, find the range of real numbers \\(x\\);

\\((2)\\) If \\(p\\) is a sufficient condition for \\(q\\), find the range of real numbers \\(a\\).

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