
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 that point $O$ is the coordinate origin, a point $A(4,3)$ is provided, and point $B(x,0)$ moves along the positive semi-axis of the $x$-axis. Let $l(x)$ represent the length of the line segment $AB$. Determine the maximum value of the ratio of the lengths of two sides in $\triangle OAB$, denoted as $\frac{x}{l(x)}$.

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