
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
Four points $C,$ $D,$ $F,$ and $M$ lie on a straight line. Point $H$ is not on the line such that $\angle CDH = 130^\circ$ and $\angle HFM = 70^\circ$. If the reflex angle at $H$ is $y^\circ$, find the value of $y$ and determine $\angle DHF$.

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