
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
The triangular pyramid \(ABCD\) intersects with the plane \(P\) along the quadrilateral \(EFGH\) such that the vertices \(E\) and \(F\) lie on the edges \(AB\) and \(AC\), respectively. It is known that the plane \(P\) is parallel to the edges \(AD\) and \(BC\), the ratio of segment \(EA\) to segment \(EB\) is 2, and the edges \(AD\) and \(BC\) are equal. Find the ratio \(EF:EH\).

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