
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
In the rectangular coordinate system $(xOy)$, three points $A(a,1)$, $B(2,b)$, and $C(3,4)$ are given. If the projections of vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$ in the direction of vector $\overrightarrow{OC}$ are the same, find the value of $3a - 4b$.

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