
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 $[x]$ denote the greatest integer less than or equal to the real number $x$. Define $R$ as the set of points $(x, y)$ that satisfy:
$$
\left\{\begin{array}{l}
x \geq 0, \\
y \geq 0, \\
x + y + [x] + [y] \leq 7
\end{array}\right.
$$
Find the area of region $R$.

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