
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]


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If the domains of the functions \( f(x) \) and \( g(x) \) are both the set of non-negative real numbers, and for any \( x \geq 0 \), \( f(x) \cdot g(x) = \min \{ f(x), g(x) \} \), given \( f(x) = 3 - x \) and \( g(x) = \sqrt{2x + 5} \), then the maximum value of \( f(x) \cdot g(x) \) is ______ .

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