
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
There is a sequence of one thousand random digits. A zero and a decimal point are placed in front of this sequence. As a result, a random number \( X \) is formed, written as a decimal fraction: \( X = 0.x_1 x_2 x_3 \ldots x_{1000} \). Find \( \mathrm{E}X \) (the expected value of \( X \)).

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