
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

Juca has fewer than 800 marbles. He likes to separate the marbles into groups of the same size. He noticed that if he forms groups of 3 marbles each, exactly 2 marbles are left over. If he forms groups of 4 marbles, 3 marbles are left over. If he forms groups of 5 marbles, 4 marbles are left over. Finally, if he forms groups of 7 marbles each, 6 marbles are left over.

(a) If Juca formed groups of 20 marbles each, how many marbles would be left over?

(b) How many marbles does Juca have?

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