
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
We use $\left[m\right]$ to represent the largest integer not greater than $m$, for example: $\left[2\right]=2$, $\left[4.1\right]=4$, $\left[3.99\right]=3$.  
$(1) [\sqrt{2}]=$____;  
$(2)$ If $[3+\sqrt{x}]=6$, then the range of $x$ is ____.

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