
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
Charlotte is playing the hit new web number game, Primle. In this game, the objective is to guess a two-digit positive prime integer between  $10$  and  $99$ , called the *Primle*. For each guess, a digit is highlighted blue if it is in the *Primle*, but not in the correct place. A digit is highlighted orange if it is in the *Primle* and is in the correct place. Finally, a digit is left unhighlighted if it is not in the *Primle*. If Charlotte guesses  $13$  and  $47$  and is left with the following game board, what is the *Primle*?  $$ \begin{array}{c} 
            \boxed{1} \,\, \boxed{3}  [\smallskipamount]
            \boxed{4}\,\, \fcolorbox{black}{blue}{\color{white}7}
       \end{array} $$  *Proposed by Andrew Wu and Jason Wang*

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