
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 function $y=f(x)$ with the domain $\{x|-3\leq x\leq 8, \text{ and } x\neq 5\}$, and the range $\{y|-1\leq y\leq 2, \text{ and } y\neq 0\}$. The following statements about the function $y=f(x)$ are given: ① When $x=-3$, $y=-1$; ② The point $(5,0)$ is not on the graph of the function $y=f(x)$; ③ Adding the point $(5,0)$ to the graph of $y=f(x)$ results in a continuous curve; ④ $y=f(x)$ is a monotonic function on the interval $[-3,5)$; ⑤ The graph of $y=f(x)$ intersects the coordinate axes at only one point. Among these, the statements that are definitely correct are.

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