
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
Candidates should choose and solve only one of the three sub-problems below. If more than one is answered, only the first one will be graded.
1. If the solution set of the inequality $|x-1|+|x-m|<2m$ is empty, the range of values for $m$ is ____________.
2. The length of the chord cut by the curve $\begin{cases} x=2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (with $\theta$ as the parameter) from the line $3x-4y-1=0$ is ____________.
3. If the incircle of the right triangle $\triangle ABC$ is tangent to the hypotenuse $AB$ at point $D$, and $AD=1$, $BD=2$, then the area of $\triangle ABC$ is ____________.

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