
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
For some positive integers $c$ and $d$, the product \[\log_c(c+2) \cdot \log_{c+2} (c+4) \dotsm \log_{d-4} (d-2)  \cdot\log_{d-2} d\] contains exactly $435$ terms, and its value is $2.$ Compute $c+d.$

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