
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
Let \( a \) and \( b \) be real numbers such that \( 17\left(a^{2}+b^{2}\right)-30ab-16=0 \). Find the maximum value of \( \sqrt{16a^{2}+4b^{2}-16ab-12a+6b+9} \).

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