
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 an arithmetic sequence $\{a_n\}$ with the first term $a_1=1$ and common difference $d=-\frac{1}{2}$, if the intersection point $M$ of the lines $x+y-3a_n=0$ and $2x-y+2a_n-1=0$ is in the fourth quadrant, then $a_n=$ ______.

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