
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
$A$ is at the foot of a mountain, $B$ is at the peak, and $C$ is a point on the slope such that $A C=\frac{1}{3} A B$. Two individuals, Jia and Yi, start from point $A$ simultaneously, reach the peak $B$, and return to point $A$, repeatedly. The ratio of their speeds is $6:5$, and both Jia's and Yi's downhill speeds are 1.5 times their respective uphill speeds. At a certain moment, Jia first sees Yi climbing on the $A C$ section while Jia is at the peak. After some time, Jia sees Yi climbing on the $A C$ section again while Jia is at the peak. How many times has Jia reached the peak when Jia sees Yi climbing on the $A C$ section for the second time (including that moment)?

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