
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
(1) There are 100 products numbered from 00 to 99. Using the systematic sampling method, 5 products are selected for inspection. The products are divided into groups, and each group selects products at the same interval. If the product selected in the 5th group has the number 94, then the number of the product selected in the 2nd group is ______.

(2) Given a set of data: 87, x, 90, 89, 93, with an average of 90, the variance of this set of data is ______.

(3) A line $l$ passing through the center $O$ of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ($a > b > 0$) intersects the ellipse at points $A$ and $B$. $F_1$ and $F_2$ are the foci of the ellipse. If the area of the parallelogram $AF_1BF_2$ is $ab$, then the range of the eccentricity of the ellipse is ______.

(4) If for any positive real numbers $x, y$, the inequality $\left( 2x-\frac{y}{e} \right)\ln \frac{y}{x}\leqslant \frac{x}{me}$ holds, then the range of the real number $m$ is ______.

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