
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 the line $l-\frac{x}{m}+\frac{y}{4-m}=1$,

(1) If the slope of line $l$ is equal to $2$, find the value of the real number $m$;

(2) If line $l$ intersects the positive semi-axes of the $x$-axis and $y$-axis at points $A$ and $B$ respectively, and $O$ is the origin, find the maximum area of $\triangle AOB$ and the equation of the line at this time.

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