
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
Non-negative real numbers  $x, y, z$  satisfy the following relations:  $3x + 5y + 7z = 10$  and  $x + 2y + 5z = 6$ .

Find the minimum and maximum of  $w = 2x - 3y + 4z$ .

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