
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 two vectors $\boldsymbol{a}$ and $\boldsymbol{b}$ such that $|\boldsymbol{a} - 2\boldsymbol{b}| = 1$ and $|2\boldsymbol{a} + 3\boldsymbol{b}| = \frac{1}{3}$, find the value of $(5\boldsymbol{a} - 3\boldsymbol{b}) \cdot (\boldsymbol{a} - 9\boldsymbol{b})$.

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