
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
A board with a mass of \( M = 4 \) kg lies on a horizontal table. A block with a mass of \( m = 1 \) kg rests on the board. The board and the block are connected by a light string that passes over a pulley. The board is acted upon by a horizontal force \( F \). The board moves with an acceleration \( a = \frac{g}{5} \). The coefficient of friction between the board and the block, as well as between the board and the table, is \( \mu = 0.2 \).

1) Find the tension in the string.
2) Find the force \( F \).

Neglect the mass of the pulley and friction in its axis. Assume \( g = 10 \) m/s\(^2\).

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