
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
Evan has  $10$  cards numbered  $1$  through  $10$ . He chooses some of the cards and takes the product of the numbers on them. When the product is divided by  $3$ , the remainder is  $1$ . Find the maximum number of cards he could have chose.

*Proposed by Evan Chang*

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