
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 diagram shows a triangle \(ABC\) and two lines \(AD\) and \(BE\), where \(D\) is the midpoint of \(BC\) and \(E\) lies on \(CA\). The lines \(AD\) and \(BE\) meet at \(Z\), the midpoint of \(AD\). What is the ratio of the length \(CE\) to the length \(EA\)?

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