
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
If $x$ is a rational number, we define $\{x\}$ as the smallest integer not less than $x$, such as $\{3.2\}=4$, $\{-2.6\}=-2$, $\{5\}=5$.  
$(1)$ According to the definition: $\{4.7\}=\_\_\_\_\_\_$, $\{-5.3\}=\_\_\_\_\_\_$;  
$(2)$ If $\{a\}=2$, directly write down the relationship between $a$ and $1$, $2$ as ______;  
$(3)$ Solve the following problems:  
① Find the range of values of $m$ that satisfy $\{-2m+7\}=-3$: ______;  
② Write down the solution to the equation $\{4.5n-2.5\}=3n+1$ directly as ______.

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