
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
Six horizontal lines and five vertical lines are drawn in a plane. Three of the horizontal lines are red, and two of the vertical lines are blue. In how many ways can four lines be chosen such that they form a rectangle, and the rectangle has sides from at least one red horizontal line and one blue vertical line?

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