
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 diagram, an equilateral triangle has a base of 10 cm. A perpendicular bisector is drawn from a vertex, bisecting the opposite side. Find both the perimeter of the triangle and the length of the bisector. 
\[ \text{[asy]}
size(100);
draw((0,0)--(10,0)--(5,5*sqrt(3))--cycle);
label("10 cm",(5,0),S);
draw((5,-.2)--(5,.2));
draw((5,5*sqrt(3))--(5,0), dashed);
label("Bisector",(5,2.5*sqrt(3)), E);
\text{[/asy]} \]

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