
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
At a significance level of 0.01, test the null hypothesis $H_{0}: F_{1}(x)=F_{2}(x)$ for the homogeneity of two samples with sizes $n_{1}=6$ and $n_{2}=7$ (the first row contains the values of the first sample; the second row contains the values of the second sample):

$$
\begin{array}{rrrrrrrr}
x_{i} & 3 & 4 & 6 & 10 & 13 & 17 & \\
y_{i} & 1 & 2 & 5 & 7 & 16 & 20 & 22
\end{array}
$$

Use the alternative hypothesis $H_{1}$ : $F_{1}(x) \neq F_{2}(x)$.

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