
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 a function $f(x)$ which satisfies $f(x) + f(y) = f(x + y) + 3$ for all real numbers $x$, $y$, and given $f(3) = 6$, when $x > 0$, we have $f(x) > 3$. What is the range of real numbers $a$ such that $f(2a + 1) < 5$?

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