
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
Denote by \( [a] \) the greatest integer less than or equal to \( a \). Let \( N \) be an integer, \( x \) and \( y \) be numbers satisfying the simultaneous equations 
\[
\begin{cases}
[x] + 2y = N + 2 \\
[y] + 2x = 3 - N
\end{cases}.
\]
Find \( x \) in terms of \( N \).

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