
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
Find the rank of the matrix using the method of bordering minors

$$
A=\left(\begin{array}{ccccc}
2 & 1 & 2 & 1 & 2 \\
1 & 1 & 5 & -2 & 3 \\
-1 & 0 & -4 & 4 & 1 \\
3 & 3 & 8 & 1 & 9
\end{array}\right)
$$

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