
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
In a harbor, the time interval between two consecutive high tides is 12 hours. The water depth during low tide is 8.4 meters, and during high tide, it is 16 meters. A high tide occurred on October 10th at 4:00. The relationship between the water depth d (in meters) and time t (in hours) can be approximated by the formula d = A * sin(ωt + φ) + h, where A > 0, ω > 0, and |φ| < $\frac{π}{2}$.

1. Starting from October 10th at 0:00, choose a trigonometric function to approximate the relationship between the water depth d (in meters) and time t (in hours) in this harbor.
2. What was the water depth in the harbor on October 10th at 17:00? (Answer accurate to 0.1 meters)
3. How long was the water depth in the harbor lower than 10.3 meters on October 10th?

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