
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
If three lines $ax + y + 3 = 0$, $x + y + 2 = 0$, and $2x - y + 1 = 0$ intersect at one point, then the value of the determinant $\begin{vmatrix} a & 1 & 3 \\ 1 & 1 & 2 \\ 2 & -1 & 1 \end{vmatrix}$ is $\_\_\_\_\_\_$.

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