
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
$EFGH$ is a square and $P$ and $N$ are the midpoints of $\overline{EF}$ and $\overline{GH},$ respectively. Find $\sin \phi.$
[asy]
unitsize(1.5 cm);

draw((0,0)--(3,0)--(3,3)--(0,3)--cycle);
draw((0,0)--(1.5,3));
draw((0,0)--(0,1.5));
label("$E$", (0,0), SW);
label("$F$", (0,3), NW);
label("$G$", (3,3), NE);
label("$H$", (3,0), SE);
label("$P$", (0,1.5), W);
label("$N$", (1.5,3), N);
label("$\phi$", (.5,.5), SW);
[/asy]

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