
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]


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Let $a$ be a positive integer. The notation $[2a+1, 2a+2, 2a+3]$ represents the least common multiple (LCM) of $2a+1$, $2a+2$, and $2a+3$, denoted as $N$. If $2a+4$ divides $N$, find $a$.

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