
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
Points $A$ and $B$ are located on two lines that intersect at an angle of $60^\circ$. The distance between the points is $31 \mathrm{~m}$. If point $A$ moves $20 \mathrm{~m}$ closer to the intersection of the lines, the distance between the points becomes $21 \mathrm{~m}$. What are the distances of the points from the intersection of the lines?

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