
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
Mike's Age. "Pat O'Connor," said Colonel Crackham, "is now \(1 \frac{1}{3}\) times as old as he was when he built the pigsty under the window of his living room. Little Mike, who was 3 years and 4 months old when Pat built the pigsty, is now 2 years older than half the age Biddy, Pat's wife, was when Pat built his pigsty. So, when little Mike reaches the age Pat was when he built the pigsty, the combined age of all three will be one hundred years. How old is little Mike now?"

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