
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
In the image, there is a number line with the numbers 10 and 30 marked, along with other unnamed points representing integers. Janek has marked his favorite number with a dot on this line along with four other numbers, and we know that

- one is half of Janek's number,
- one is 6 more than Janek's number,
- one is 10 less than Janek's number,
- one is twice Janek's number.

Determine what Janek's favorite number is.

(S. Bednářová)

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