
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 $f(x) = 5^{5x}, g(x) = \log_{5}\left(\frac{x}{5}\right), h_1(x) = g(f(x))$, and $h_n(x) = h_1(h_{n-1}(x))$ for integers $n \geq 2$. Calculate $h_{10}(2)$.
**A** $2 \cdot 5^{10} - \frac{5^{10} - 1}{4}$  
**B** $2 \cdot 5^{9} - \frac{5^9 - 1}{4}$  
**C** $2 \cdot 5^{11} - \frac{5^{11} - 1}{4}$  
**D** $2 \cdot 5^8 - \frac{5^{8} - 1}{4}$

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