
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
When the weather is clear, the farthest distance $S$ (unit: $km$) a person can see the sea can be estimated by the formula $S^{2}=1.7h$ meters, where $h$ (unit: $m$) is the height of the eyes above the sea level.<br/>$(1)$ If a person stands on the shore and the height of the eyes above the sea level is $1.7m$, how far can they see?<br/>$(2)$ If they climb up an observation tower to make the farthest distance they can see four times that in $(1)$, and the height from their eyes to the ground is $1.5m$, what is the height of the observation tower above the sea level?

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