
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
Suppose  $b > 1$  is a real number where  $\log_5 (\log_5 b + \log_b 125) = 2$ . Find  $log_5 \left(b^{\log_5 b}\right) + log_b \left(125^{\log_b 125}\right).$ 

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