
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
Given that $a$, $b$, and $a+m$ are all real numbers greater than $0$, consider the following five statements:<br/>①$a \gt b$, ②$a \lt b$, ③$m \gt 0$, ④$m \lt 0$, ⑤$\frac{{b+m}}{{a+m}} \gt \frac{b}{a}$. If two of these statements are true, choose one of the remaining statements as the conclusion and write a correct proposition.

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