
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 triangle $ABC$, the perpendicular drawn from $A_{0}$, the midpoint of side $BC$, to the angle bisector starting from $A$ intersects the rays $AB$ and $AC$ at points $D_{1}$ and $D_{2}$, respectively. The circle with diameter $D_{1} D_{2}$ has a chord $E_{1} E_{2}$ perpendicular to $D_{1} D_{2}$ and passing through $A_{0}$. Examine the size relationship between $E_{1} E_{2}$ and $BC$.

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