
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
Jennifer has collected one of each of the first 26 state quarters in the order they joined the union. The chart depicts the number of states that joined the union in each decade. What fraction of Jennifer's 26 quarters represents states that joined the union during the decade from 1800 to 1809? Express your answer as a common fraction.

[asy]
size(200);
label("1780",(6,0),S);
label("1800",(12,-12),S);
label("1820",(18,0),S);
label("1840",(24,-12),S);
label("1860",(30,0),S);
label("1880",(36,-12),S);
label("1900",(42,0),S);
label("1950",(48,-12),S);
label("to",(6,-4),S);
label("to",(12,-16),S);
label("to",(18,-4),S);
label("to",(24,-16),S);
label("to",(30,-4),S);
label("to",(36,-16),S);
label("to",(42,-4),S);
label("to",(48,-16),S);
label("1789",(6,-8),S);
label("1809",(12,-20),S);
label("1829",(18,-8),S);
label("1849",(24,-20),S);
label("1869",(30,-8),S);
label("1889",(36,-20),S);
label("1909",(42,-8),S);
label("1959",(48,-20),S);
draw((0,0)--(50,0));
draw((0,2)--(50,2));
draw((0,4)--(50,4));
draw((0,6)--(50,6));
draw((0,8)--(50,8));
draw((0,10)--(50,10));
draw((0,12)--(50,12));
draw((0,14)--(50,14));
draw((0,16)--(50,16));
draw((0,18)--(50,18));
fill((4,0)--(8,0)--(8,8)--(4,8)--cycle,gray(0.8));  // Adjusted
fill((10,0)--(14,0)--(14,8)--(10,8)--cycle,gray(0.8)); // Adjusted with 8 states in 1800-1809
fill((16,0)--(20,0)--(20,9)--(16,9)--cycle,gray(0.8));
fill((22,0)--(26,0)--(26,5)--(22,5)--cycle,gray(0.8));
fill((28,0)--(32,0)--(32,9)--(28,9)--cycle,gray(0.8));
fill((34,0)--(38,0)--(38,6)--(34,6)--cycle,gray(0.8));
fill((40,0)--(44,0)--(44,3)--(40,3)--cycle,gray(0.8));
[/asy]

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