
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
Let $m$ and $n$ be integers greater than $0$, and $3m + 2n = 225$.
(1) If the greatest common divisor of $m$ and $n$ is $15$, then $m + n =$    ;
(2) If the least common multiple of $m$ and $n$ is $45$, then $m + n =$    .

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