
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
Roger has exactly one of each of the first 30 states' new U.S. quarters. These quarters were released in the same order that the states joined the union. The graph below shows the number of states that joined the union in each decade, represented in a new format. Determine the fraction of Roger's 30 quarters that represents states which joined the union during the decade 1860 through 1869. 

[asy]
size(200);
label("1860",(10,0),S);
label("1880",(20,-12),S);
label("1900",(30,0),S);
label("1920",(40,-12),S);
label("1940",(50,0),S);
label("1960",(60,-12),S);
label("to",(10,-16),S);
label("to",(20,-4),S);
label("to",(30,-16),S);
label("to",(40,-4),S);
label("to",(50,-16),S);
label("to",(60,-4),S);
label("1869",(10, -20),S);
label("1889",(20, -8),S);
label("1909",(30, -20),S);
label("1929",(40, -8),S);
label("1949",(50, -20),S);
label("1969",(60, -8),S);
draw((0,0)--(65,0));
draw((0,2)--(65,2));
draw((0,4)--(65,4));
draw((0,6)--(65,6));
draw((0,8)--(65,8));
draw((0,10)--(65,10));
draw((0,12)--(65,12));
draw((0,14)--(65,14));
draw((0,16)--(65,16));
draw((0,18)--(65,18));
fill((8,0)--(12,0)--(12,8)--(8,8)--cycle,gray(0.8)); 
fill((18,0)--(22,0)--(22,7)--(18,7)--cycle,gray(0.8));
[/asy]

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