
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
Junior and Carlson ate a barrel of jam and a basket of cookies, starting and finishing at the same time. Initially, Junior ate the cookies and Carlson ate the jam, then (at some point) they switched. Carlson ate both the jam and the cookies three times faster than Junior. What fraction of the jam did Carlson eat, given that they ate an equal amount of cookies?

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