
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  $R > 0$ , be an integer, and let  $n(R)$  be the number um triples  $(x, y, z) \in \mathbb{Z}^3$  such that   $2x^2+3y^2+5z^2 = R$ . What is the value of $\lim_{ R \to \infty}\frac{n(1) + n(2) + \cdots + n(R)}{R^{3/2}}$ ?

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