
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
Define a function $f(x)$ for positive integer values of $x$ by
\[
f(x) = \left\{
\begin{aligned}
\log_3 x & \quad \text{if } x \text{ is a multiple of 3 and not of 5} \\
\log_5 x & \quad \text{if } x \text{ is a multiple of 5 and not of 3} \\
\log_{15} x & \quad \text{if } x \text{ is a multiple of both 3 and 5} \\
1 + f(x + 1) & \quad \text{otherwise}
\end{aligned}
\right.
\]
Compute $f(100)$.

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