
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 $p: 4x^2+12x-7 \leq 0$, $q: a-3 \leq x \leq a+3$.
1. When $a=0$, if $p$ is true and $q$ is false, find the range of real numbers for $x$.
2. If $p$ is a sufficient condition for $q$, find the range of real numbers for $a$.

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