
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 the diagram, $P$ and $Q$ start at the positions shown and point $X$ is fixed on the circle. Initially, the shortest distance along the circumference from $P$ to $X$ is $8 \mathrm{~m}$, from $Q$ to $X$ is $16 \mathrm{~m}$, and from $P$ to $Q$ is $16 \mathrm{~m}$. $P$ and $Q$ move around the circle in opposite directions as indicated by the arrows. $P$ moves at $3 \mathrm{~m} / \mathrm{s}$. $Q$ moves at $3.5 \mathrm{~m} / \mathrm{s}$. If $P$ and $Q$ begin moving at the same time, after how many seconds do $P$ and $Q$ meet at $X$?

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