
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  $a$  and  $b$  be real numbers greater than 1 such that  $ab=100$ . The maximum possible value of  $a^{(\log_{10}b)^2}$  can be written in the form  $10^x$  for some real number  $x$ . Find  $x$ .

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