
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 the sum of the coefficients of the expansion of $(3x+ \sqrt{x})^{n}$ be $M$, and the sum of the binomial coefficients be $N$. If $M-N=240$,  
(1) find $n$;  
(2) find all the rational terms of $x$ in the expansion.

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