
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 the isosceles right triangle \(\triangle ABC\), \(AD\) is the median of the right angle side \(BC\) and \(BE\) is perpendicular to \(AD\) intersecting \(AC\) at point \(E\). \(EF\) is perpendicular to \(BC\). If \(AB = BC = a\), calculate the length of \(EF\).

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