
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
Independent measurements of the angles of a triangle $x_{1}, x_{2}, x_{3}$ gave results $x_{1}^{*}=31^{\circ}, x_{2}^{*}=62^{\circ}, x_{3}^{*}=89^{\circ}$. It is known that $x_{1}+x_{2}+x_{3}-180^{\circ}=0$. Use this equality to refine the values $x_{1}^{*}, x_{2}^{*}, x_{3}^{*}$, assuming the measurement errors of the angles $x_{1}, x_{2}, x_{3}$ are normally distributed with zero mean and variances $\sigma_{1}^{2}=\sigma_{2}^{2}=\sigma_{3}^{2}=\left(0.1^{\circ}\right)^{2}$.

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