
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
Let $\mu$ be an arbitrary measure, and let $\xi$ and $\eta$ be extended random variables, for which $\int_{\Omega}|\xi| d \mu$ and $\int_{\Omega}|\eta| d \mu$ are finite. Then if the inequality $\int_{A} \xi d \mu \leqslant \int_{A} \eta d \mu$ holds for all sets $A \in \mathscr{F}$, it follows that $\mu(\xi > \eta) = 0$.

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