
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
Three jars each contain the same number of marbles, and each marble is either blue or green. In Jar $1$ the ratio of blue to green marbles is $7:3$, in Jar $2$ it is $6:4$, and in Jar $3$ it is $5:5$. There are a total of $240$ green marbles across all jars. Calculate the difference in the number of blue marbles in Jar $1$ and Jar $3$.

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