
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
Let  $a, b, c, d, e \in \mathbb{R}^+$  and  $f:\{(x, y) \in (\mathbb{R}^+)^2|c-dx-ey > 0\}\to \mathbb{R}^+$  be given by  $f(x, y) = (ax)(by)(c- dx- ey)$ . 
Find the maximum value of  $f$ .

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