
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 the set of possible values for the discrete random variable \( X \): \( x_{1}=-1, x_{2}=0, x_{3}=1 \), and the expectations of this variable and its square: \( M(X)=0.1 \) and \( M\left(X^{2}\right)=0.9 \), find the probabilities \( p_{1}, p_{2}, p_{3} \) corresponding to the possible values \( x_{1}, x_{2}, x_{3} \).

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