
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
Two hikers start at points $A$ and $B$, which are $100$ miles apart. They head towards each other, starting at the same time. The hiker at $A$ walks uniformly at the rate of $5$ miles per hour. The hiker at $B$ starts walking at a rate of $4$ miles per hour and increases their speed by $0.25$ miles per hour every subsequent hour. Determine the point of intersection.

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