
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 $ABC$ with $AB=AC$, the altitude $AD$ bisects the base $BC$. Given that $AB = AC = 13$ units and the total length of base $BC = 10$ units, determine the area of $\triangle ABC$.

[asy]
draw((0,0)--(10,0)--(5,12)--cycle,black+linewidth(1));
draw((5,12)--(5,0),black+linewidth(1)+dashed);
draw((5,0)--(5,1)--(4,1)--(4,0)--cycle,black+linewidth(1));
label("$A$",(5,12),N);
label("$B$",(0,0),SW);
label("$C$",(10,0),SE);
label("$D$",(5,0),S);
label("13",(0,0)--(5,12),NW);
label("13",(5,12)--(10,0),NE);
label("10",(5,-1));
[/asy]

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