
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 triangle \( ABC \) has \( AC = 1 \), \(\angle ACB = 90^\circ\), and \(\angle BAC = \varphi\). \( D \) is the point between \( A \) and \( B \) such that \( AD = 1 \). \( E \) is the point between \( B \) and \( C \) such that \(\angle EDC = \varphi\). The perpendicular to \( BC \) at \( E \) meets \( AB \) at \( F \). Find \(\lim_{\varphi \to 0} EF\).

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