
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
Denote by  $d(n)$  the number of positive divisors of a positive integer  $n$ . Find the smallest constant  $c$  for which  $d(n)\le c\sqrt n$  holds for all positive integers  $n$ .

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