
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 that the graph of the power function $f(x)$ passes through the point $(\frac{1}{8}, \frac{\sqrt{2}}{4})$, and $P(x_1, y_1)$, $Q(x_2, y_2) (x_1 < x_2)$ are any two different points on the function graph, provide the following conclusions:
$①x_1f(x_1) > x_2f(x_2)$;
$②x_1f(x_1) < x_2f(x_2)$;
$③\frac{f(x_1)}{x_1} > \frac{f(x_2)}{x_2}$;
$④\frac{f(x_1)}{x_1} < \frac{f(x_2)}{x_2}$.
The sequence number of the correct conclusions is $\_\_\_\_\_\_$.

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