
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
Alice's age is 20 more than the sum of Ben's age and Cindy's age. Additionally, the square of Alice's age is 2050 more than the square of the sum of Ben's and Cindy's age. Determine the sum of the ages of Alice, Ben, and Cindy.

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