
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 \( f(x) = |x - a| + |x - 15| + |x - a - 15| \), where \( a \leq x \leq 15 \) and \( 0 < a < 15 \). If \( Q \) is the smallest value of \( f(x) \), find the value of \( Q \).

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