
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
What are the smallest and largest values of the expression \( K = 5x - 6y + 7z \) if \( x, y, \) and \( z \) are non-negative numbers that satisfy

\[ 4x + y + 2z = 4 \]

and

\[ 3x + 6y - 2z = 6? \]

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