
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
You are playing a game called "Hovse." 
Initially you have the number  $0$  on a blackboard.
If at any moment the number  $x$  is written on the board, you can either: $\bullet$  replace  $x$  with  $3x + 1$  $\bullet$  replace  $x$  with  $9x + 1$  $\bullet$  replace  $x$  with  $27x + 3$  $\bullet$  or replace  $x$  with  $\left \lfloor \frac{x}{3} \right \rfloor $ .
However, you are not allowed to write a number greater than  $2017$  on the board. How many positive numbers can you make with the game of "Hovse?"

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