
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
We define  $I(n)$  as the result when the digits of  $n$  are reversed. For example,  $I(123)=321$ ,  $I(2008)=8002$ . Find all integers  $n$ ,  $1\leq{n}\leq10000$  for which  $I(n)=\lceil{\frac{n}{2}}\rceil$ .
Note:  $\lceil{x}\rceil$  denotes the smallest integer greater than or equal to  $x$ . For example,  $\lceil{2.1}\rceil=3$ ,  $\lceil{3.9}\rceil=4$ ,  $\lceil{7}\rceil=7$ .


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