
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 the sets $A=\left\{ x\in\mathbb{R} \mid |x+3|+|x-4|\leqslant 9\right\}$ and $B=\left\{ x\in\mathbb{R} \mid x=4t+ \frac{1}{t}-6, t\in(0,+\infty)\right\}$, then the intersection of sets $A$ and $B$ is $\boxed{\{x|-2\leqslant x\leqslant 5\}}$.

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