
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
Given that the connection from $P$ leads to $R$ or $S$, with $R$ offering paths to $T$ or $U$, and with $T$ and $U$ leading directly to $Q$, $S$ offering paths to $T$, $U$, and directly to $Q$, and $P$ offering a direct path to $Q$, determine the total number of different routes from $P$ to $Q$.

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