
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
A square piece of paper \(A B C D\) is white on one side and grey on the other side. Initially, the paper is flat on a table with the grey side down. Point \(E\) is on \(BC\) so when the paper is folded along \(AE\), point \(B\) lands on diagonal \(AC\). Similarly, point \(F\) is on \(DC\) so that when the paper is folded along \(AF\), point \(D\) lands on \(AC\). After these folds, the resulting shape is kite \(AECF\). What fraction of the area of \(AECF\) is grey?

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