
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
Compute the number of integers  $1 \leq n \leq 1024$  such that the sequence  $\lceil n \rceil$ ,  $\lceil n/2 \rceil$ ,  $\lceil n/4 \rceil$ ,  $\lceil n/8 \rceil$ ,  $\ldots$  does not contain any multiple of  $5$ . 

*Proposed by Sean Li*

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