
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 any isosceles triangle $PQR$ with $PQ = PR$, the altitude $PS$ bisects the base $QR$ so that $QS = RS$. Given that the triangle sides are $PQ = PR = 15$ and the entire base length $QR = 20$.

[asy]
draw((0,0)--(20,0)--(10,36)--cycle,black+linewidth(1));
draw((10,36)--(10,0),black+linewidth(1)+dashed);
draw((10,0)--(10,1)--(9,1)--(9,0)--cycle,black+linewidth(1));
draw((4.5,-4)--(0,-4),black+linewidth(1));
draw((4.5,-4)--(0,-4),EndArrow);
draw((15.5,-4)--(20,-4),black+linewidth(1));
draw((15.5,-4)--(20,-4),EndArrow);
label("$P$",(10,36),N);
label("$Q$",(0,0),SW);
label("$R$",(20,0),SE);
label("$S$",(10,0),S);
label("15",(0,0)--(10,36),NW);
label("15",(10,36)--(20,0),NE);
label("20",(10,-4));
[/asy]

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