
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 inequalities \( -1 \leqslant 2x + y - z \leqslant 8 \), \( 2 \leqslant x - y + z \leqslant 9 \), and \( -3 \leqslant x + 2y - z \leqslant 7 \), find the maximum and minimum values of the function \( f(x, y, z) = 7x + 5y - 2z \).

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