
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
Luke and Carissa are finding the sum of the first  $20$  positive integers by adding them one at a time. Luke forgets to add a number and gets an answer of  $207$ . Carissa adds a number twice by mistake and gets an answer of  $225$ . What is the sum of the number that Luke forgot and the number that Carissa added twice?

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