
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
A car travels at a constant speed of $x$ kilometers per hour on the highway (considering highway safety requirements $60 \leq x \leq 120$). The fuel consumption per hour (the amount of gasoline needed) is $\frac{1}{5}(x - k + \frac{4500}{x})$ liters, where $k$ is a constant and $60 \leq k \leq 100$.

1. When the car travels at a speed of $120$ kilometers per hour, the fuel consumption per hour is $11.5$ liters. To ensure that the fuel consumption does not exceed $9$ liters per hour, find the range of values for $x$.
2. Find the minimum fuel consumption for the car to travel $100$ kilometers.

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