
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
(1) Given that $0 < x < \dfrac{4}{3}$, find the maximum value of $x(4-3x)$.

(2) Point $(x,y)$ moves along the line $x+2y=3$. Find the minimum value of $2^{x}+4^{y}$.

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