
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
If 5 identically shaped and sized colored eggs are randomly drawn from a box, where 2 are yellow, 2 are red, and 1 is purple, calculate the probability that the two drawn eggs are exactly 1 red and 1 yellow.

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