
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
Three positive real numbers  $a, b, c$  satisfy  $a^b = 343, b^c = 10, a^c = 7.$  Find  $b^b.$   $$ \mathrm a. ~ 1000\qquad \mathrm b.~900\qquad \mathrm c. ~1200 \qquad \mathrm d. ~4000 \qquad \mathrm e. ~100 $$  

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