
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
Consider six different digits $A, B, C, P, Q, R$ selected from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. First, find the maximum value of the sum $\frac{A}{B} + \frac{C}{P}$. Second, using the digits not used in the first part, find the minimum value of $\frac{Q}{R} + \frac{P}{C}$.

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