
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
The two numbers  $0$  and  $1$  are initially written in a row on a chalkboard. Every minute thereafter, Denys writes the number  $a+b$  between all pairs of consecutive numbers  $a$ ,  $b$  on the board. How many odd numbers will be on the board after  $10$  such operations?

*Proposed by Michael Kural*

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