
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 a coordinate system with optional questions on parametric equations, it is known that the line $l_1$ defined by the parametric equations $\begin{cases} x = 1 + 3t \\ y = 2 - 4t \end{cases}$ (where $t$ is a parameter) intersects with line $l_2$ described by the equation $2x - 4y = 5$ at point $B$. Given point $A(1,2)$, find the distance $|AB|$.

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