
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
Draw an isosceles triangle with area $t$ inside an equilateral triangle $ABC$, such that the vertex $C_1$ of the isosceles triangle lies at the midpoint of side $AB$. At what distance from side $AB$ does the base $A_1 B_1$ of the isosceles triangle intersect the sides $AC$ and $BC$?

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