
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
An infinite sequence of circles is composed such that each circle has a decreasing radius, and each circle touches the subsequent circle and the two sides of a given right angle. Calculate the ratio of the area of the first circle to the sum of the areas of all subsequent circles in the sequence.

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