
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
In the Cartesian coordinate plane $(xOy)$, let the curve $y=2x-\frac{m}{x}$ $(m \in \mathbb{R}, m \neq -2)$ have a tangent line $l$ at $x=1$. If the sum of the intercepts of the line $l$ on the two coordinate axes is $12$, then the value of $m$ is _______.

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