
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
Solve the following system of equations, where \(a\), \(b\), and \(c\) are bases of number systems, and for example, \({ }^{a)} 101\) represents the number written as \(1,0,1\) in base \(a\):

\[
\begin{aligned}
& { }^{a)} 101+{ }^{b)} 201={ }^{c)} 39+9, \\
& { }^{a)} 203+{ }^{b)} 404={ }^{c)} 77+8 .
\end{aligned}
\]

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