
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
What is the distance between Budapest and Rozsnyó if the latitude and longitude of Budapest are $\varphi = 47^{\circ} 29^{\prime} 15^{\prime \prime}$ and $\lambda = 36^{\circ} 42^{\prime} 17^{\prime \prime}$, respectively, and the latitude and longitude of Rozsnyó are $\varphi^{\prime} = 40^{\circ} 39^{\prime} 2^{\prime \prime}$ and $\lambda^{\prime} = 38^{\circ} 12^{\prime} 28^{\prime \prime}$, respectively? How much longer is the longest day in Rozsnyó compared to the longest day in Budapest, if the declination is $\delta = 23^{\circ} 27^{\prime} 55^{\prime \prime}$?

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