
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
There are nine cards that have the digits  $1, 2, 3, 4, 5, 6, 7, 8$  and  $9$  written on them, with one digit on each card. Using all the cards, some numbers are formed (for example, the numbers  $8$ ,  $213$ ,  $94$ ,  $65$  and  $7$ ).
a) If all the numbers formed are prime, determine the smallest possible value of their sum.
b) If all formed numbers are composite, determine the smallest possible value of their sum.

Note: A number  $p$  is prime if its only divisors are  $1$  and  $p$ . A number is composite if it has more than two dividers. The number  $1$  is neither prime nor composite.

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