
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
An observer is standing on Gellérthegy. His eyes are on the plane defined by the southern edges of the two towers of the Elizabeth Bridge. He sees the vertical edge of the southern side of one tower (from the road surface to the highest point) at an angle of $\alpha$, and the southern side of the other tower at an angle of $\beta$. How high is the observer above the horizontal plane that passes through the bases of the towers, if the distance between the two towers is $d$ meters and their considered height is $m$ meters? Given: $d=290 \text{ m}$, $m=40 \text{ m}$, $\alpha=11.4^{\circ}$, $\beta=4.7^{\circ}$.

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