
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 any two positive real numbers $a$ and $b$, then $a \Diamond b$ is defined such that $(ab) \Diamond b = a(b \Diamond b)$ and $(a \Diamond 1) \Diamond a = a \Diamond 1$. Knowing $1 \Diamond 1 = 1$, find the value of $\frac{1}{2} \Diamond \frac{4}{3}$.

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