
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
(Coordinate Systems and Parametric Equations - Optional Problem)
Given the line $l\_1: \begin{cases} x=1+3t \\ y=2-4t \end{cases} (t$ is the parameter$) and the line $l\_2$: $2x-4y=5$ intersect at point $B$, and point $A(1,2)$, then $|AB|=$ \_\_\_\_\_\_.

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