
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 value of  $a+b$  given that  $(a,b)$  is a solution to the system \begin{align*}3a+7b&=1977,5a+b&=2007.\end{align*} $\begin{array}{c@{\hspace{14em}}c@{\hspace{14em}}c} \textbf{(A) }488&\textbf{(B) }498&\end{array}$ 

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