
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
You are trying to maximize a function of the form  $f(x, y, z) = ax + by + cz$ , where  $a$ ,  $b$ , and  $c$  are constants. You know that  $f(3, 1, 1) > f(2, 1, 1)$ ,  $f(2, 2, 3) > f(2, 3, 4)$ , and  $f(3, 3, 4) > f(3, 3, 3)$ . For  $-5 \le x,y,z \le 5$ , what value of  $(x,y,z)$  maximizes the value of  $f(x, y, z)$ ? Give your answer as an ordered triple.

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