
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
If discrete random variables \( X \) and \( Y \) satisfy
\[
2 \leqslant X \leqslant 3 \text{, and } XY=1,
\]
then the maximum value of \(\mathrm{E}(X) \mathrm{E}(Y)\) is

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