
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
The Vaskapu, rising above the town of Esztergom, appears at an angle of $6^{\circ} 50^{\prime} 33^{\prime \prime}$ from point $A$ near the railway station, and at an angle of $7^{\circ} 25^{\prime} 52^{\prime \prime}$ from $200$ meters closer. From the same point $A$, the Sashegy appears at an angle of $5^{\circ} 24^{\prime} 52^{\prime \prime}$, and at an angle of $5^{\circ} 55^{\prime} 36^{\prime \prime}$ from $200$ meters closer. The angle between the horizontal lines originating from point $A$ towards the peaks is $31^{\circ} 4^{\prime} 34^{\prime \prime}$. What is the distance between the two mountain peaks?

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