
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
How many ten-digit whole numbers satisfy the following property: they have only  $2$  and  $5$  as digits, and there are no consecutive  $2$ 's in the number (i.e. any two  $2$ 's are separated by at least one  $5$ )?

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