
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
Find the coordinates of the intersection point $B$ of line $l_{1}$: $\begin{cases} x=1+3t \\ y=2-4t \end{cases}$ ($t$ is a parameter) and line $l_{2}$: $2x-4y=5$, as well as the distance between point $B$ and point $A(1,2)$.

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