
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

Find the coordinates of the vector

\[ 
X = \left( \begin{array}{l} 
x_{1} \\ 
x_{2} \\ 
x_{3} 
\end{array} \right) 
\]

if the linear transformation that maps it to vector

\[ 
Y = \left( \begin{array}{l} 
1 \\ 
2 \\ 
3 
\end{array} \right) 
\]

is given by the system of equations

\[ 
\left\{ 
\begin{array}{l} 
x_{1} + 2 x_{2} + 3 x_{3} = 1 \\ 
-x_{1} + 3 x_{2} + 4 x_{3} = 2 \\ 
2 x_{1} - 3 x_{2} + 5 x_{3} = 3 
\end{array} 
\right. 
\]

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