
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 equation \(5 x_{1} + 6 x_{2} - 7 x_{3} + 4 x_{4} = 1\), calculate the minimum value of \(3 x_{1}^{2} + 2 x_{2}^{2} + 5 x_{3}^{2} + x_{4}^{2}\).

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