
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
Minimize \(\boldsymbol{F}=\boldsymbol{x}_{2}-\boldsymbol{x}_{1}\) for non-negative \(x_{1}\) and \(x_{2}\), subject to the system of constraints:

$$
\left\{\begin{aligned}
-2 x_{1}+x_{2}+x_{3} &=2 \\
x_{1}-2 x_{2}+x_{4} &=2 \\
x_{1}+x_{2}+x_{5} &=5
\end{aligned}\right.
$$

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