
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
Find all positive pairs $(a, b)$ such that there exists a right triangle \( \triangle CDE \) with points \( A \) and \( B \) on the hypotenuse \( DE \) satisfying \( \overrightarrow{DA} = \overrightarrow{AB} = \overrightarrow{BE} \) and \( AC = a \), \( BC = b \).

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