
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
Estimate the number of 2016-digit squares. There are at least

$$
10^{2016 / 2} - 10^{2015 / 2} - 1 > 10^{1000}.
$$

The number of different sets of 2016 digits is not more than the sets where each digit appears no more than 2016 times, i.e., $2017^{10}$. Therefore, there exists such a set of 2016 digits, permutations of which can produce at least $10^{1000} / 2017^{10} > 10^{1000} / 10^{100} = 10^{900}$ squares, and certainly 2016.

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