
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 ratio \(\frac{b}{a}\) when the matrix**
\[
\begin{pmatrix} \frac{1}{20} & -\frac{9}{20} \\ -\frac{9}{20} & \frac{16}{20} \end{pmatrix}
\]
**projects onto the vector \(\begin{pmatrix} a \\ b \end{pmatrix}\).**

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