
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

The distribution of characteristics $X, Y$, and $Z$ among members of a certain statistical population is given in the following table:

| $X$ | 1 | 1 | 2 | 2 | 3 | 3 | 3 | 4 | 5 | 5 | 6 | 7 | 7 | 8 |
| :---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| $Y$ | 5 | 3 | 2 | 4 | 5 | 5 | 6 | 7 | 8 | 8 | 8 | 7 | 8 | 10 |
| $Z$ | -2 | -4 | -1 | -3 | -3 | -4 | -4 | -6 | -7 | -6 | -9 | -8 | -8 | -10 |
| $m$ | 1 | 2 | 3 | 3 | 2 | 4 | 3 | 2 | 3 | 1 | 2 | 1 | 2 | 1 |

Find the multiple linear correlation coefficient $R_{Z, X Y}$ and the partial correlation coefficients $r_{Y}(Z, X)$ and $r_{X}(Z, Y)$.

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