
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
Line segments \( AB \) and \( CD \) are situated between two parallel planes \( \alpha \) and \( \beta \). \( AC \subset \alpha \) and \( BD \subset \beta \). Given \( AB \perp \alpha \), \( AC = BD = 5 \), \( AB = 12 \), and \( CD = 13 \). Points \( E \) and \( F \) divide \( AB \) and \( CD \) in the ratio \( 1:2 \) respectively. Find the length of the line segment \( EF \).

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