
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
The base of an isosceles triangle is 8 cm, and the legs are 12 cm each. Find the length of the segment connecting the points where the angle bisectors of the angles at the base intersect the legs of the triangle.

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