
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
A nonnegative integer  $n$  is said to be  $\textit{squarish}$  is it satisfies the following conditions: $\textbf{(i)}$  it contains no digits of  $9$ ; $\textbf{(ii)}$  no matter how we increase exactly one of its digits with  $1$ , the outcome is a square.

Find all squarish nonnegative integers. $\textit{(Vlad Robu)}$ 

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