
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
$A$ walks daily from $P$ to $Q$ covering $30$ km each day. After covering $72$ km, $B$ starts walking from $Q$ to $P$ on the same path, covering $\frac{1}{10}$ of the total distance each day. After walking for a number of days equivalent to $\frac{1}{8}$ of the daily km covered, $B$ meets $A$. What is the distance between $P$ and $Q$?

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