
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
At a mathematics club meeting, kids were introduced to the following mathematical trick:

Write any number,
I will look at it
And then I will put a piece of paper
In an envelope in front of you.
 
Under your number, write another number,
And I will allow myself
To write one number as well.

We will draw a line and add
Our series of numbers.
No mistakes? Be careful?!
Is everything in order? I'm very happy!

Check the sum, please!
I had it in the envelope long ago!
 
What is the trick here? What is the secret?
Please, let me know your answer.

Try to uncover the secret of this trick.

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