
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 0.05, test the null hypothesis of homogeneity of two samples with sizes \( n_{1}=40 \) and \( n_{2}=50 \) against the alternative hypothesis \( H_{1}: F_{1}(x) \neq F_{2}(x) \), given that in the combined rank order from both samples, the sum of the ranks of the first sample variants is \( W_{\text{observed}}=1800 \).

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