
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
In a sample of size \( n = 10 \), the sample Spearman rank correlation coefficient \( \rho_{\mathrm{e}} \) was calculated to be 0.64 between students' scores on two tests. At a significance level of 0.01, test the null hypothesis that the population Spearman rank correlation coefficient is zero. In other words, determine whether the rank correlation between the test scores is significant.

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