
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
Two vectors \(\boldsymbol{a}\) and \(\boldsymbol{b}\) satisfy \(|\boldsymbol{a}-2\boldsymbol{b}|=1\) and \(|2\boldsymbol{a}+3\boldsymbol{b}|=\frac{1}{3}\). Find the value of \((5\boldsymbol{a} - 3\boldsymbol{b})(\boldsymbol{a} - 9\boldsymbol{b})\).

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