
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
In the diagram below, how many different routes are there from point  $M$  to point  $P$  using only the line segments shown?  A route is not allowed to intersect itself, not even at a single point.
[asy]
unitsize(40);
draw( (1, 0) -- (2, 0) -- (2, 1) -- (3, 1) -- (3, 2) -- (2, 2) -- (2, 3) -- (1, 3) -- (1, 2) -- (0, 2) -- (0, 1) -- (1, 1) -- cycle);
draw( (1, 1) -- (2, 1) -- (2, 2) -- (1, 2) -- cycle);
draw( (1, 0) -- (2, 1));
draw((1, 1) -- (2, 2));
draw((1, 2) -- (2, 3));
label( " $M$ ", (1, 0), SW);
label(" $P$ ", (1, 3), NW);
label(" $F$ ", (2, 3), NE);
label(" $G$ ", (2, 0), SE);
[/asy]

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